R,
General Observations:
I'm assuming both customer and provider are internal, i.e. the 'charge' is based on an internal transfer pricing scheme and that services using the contact center in fact hold their own P&L, so that their the charge backs will have a measurable impact. If this is a new scheme, expect howls and gnashing of teeth from the P&L owners as it comes straight from their current bottom line.
As a general rule, internal transfer pricing is notoriously difficult to get right because there is no market. Cost centers without external competition have a tendency to focus on their internal concerns. If they are a corporate resource total capacity and utilization represent corporate resource allocation decisions that don't map well to the price mechanism.
To the point:
If you are well down stream of such considerations, the most sucessful chargeback operations start by providing a built in price advantage over external sources (from corporate contribution) and treat organizational users as they would external customers by competing on quality. That means creating a service agreement with each organizational user covering capacity, call SLA's, and setup and change management.
In the case of a call center the important factors are total capacity, number and mix of customers to average capacity fluctuations, cost of setup and change management for call responses scripts, and cost of management and reporting setup. Specialized training for some subset of the total capacity provides an extra setup and maintenance cost, and extra capacity type to consider. What customers are probably looking for is a stable cost, SLA's up to some defined peak capacity.
Since the customer set is limited, the key cost driver for the call center is the total capacity. Under or over capacity is a risk the call center isn't in a position ot manage. Using
(staffing costs + overhead costs)/staff minutes = cost per minute
assumes that the call center sets the capacity. This leaves the customers over charged (per minute) and the center underfunded if they have too much staff. Even worse if under staffed because the callers will not be serviced.
The best option is transfering the risk to the customer in the form of a price per capacity. If the customer load is well characterized as to time per call, capacity measured by calls/period may be suitable. This is, however, another risk that the customer should be in the best position to mitigate (through their customer management, script design, etc) so a capacity measured by FTE might be best. This is a fairly common strategy that allows each customer access to the entire current excess capacity, with 'fair share' limits only when the total capacity is exceeded.
Setup, change and consulting services can be split out. The draw here is to pull the experts into the center and then share them "at cost". It is a net win for the customer to eliminate 1 FTE then pay 0.2 FTE of higher skill for the 0.1 FTE of work needed. Either fixed price per job or resource per hour or day can be used depending on the standardization of the particular service.
It's worth noting that that this scheme fits well into the usual enterprise planning cycle where each organization would make it's claim on corporate resources such as call capacity and adjusting overall budgets and capacities to meet the corporate and organization needs and goals. The accounting is just done differently.